Market-Based Asset Price Probability

Abstract: We consider volume weighted average price (VWAP) as the 1st market-based statistical moment and derive the dependence of higher statistical moments of price on statistical moments and correlations of the values and volumes of market trades. If all trade volumes are constant during the averaging interval, then the market-based statistical moments equal the frequency-based. We approximate market-based probability of price by a finite number of statistical moments. The use of VWAP results in zero price-volume correlations. We derive the expressions of market-based correlations between prices and squares of trade volumes and between squares of prices and volumes. To forecast market-based averages and volatility of asset prices, one should predict two statistical moments and the correlation of their trade values and volumes. We explain how that limits the number of predicted statistical moments of prices by the first two and limits the accuracy of the forecasts of the probability of asset prices by the accuracy of the Gaussian approximations. To improve the accuracy and reliability of large macroeconomic and market models like those developed by BlackRock's Aladdin, JP Morgan, and the U.S. Fed., the developers should use market-based statistical moments of asset prices.